# Derive an expression for marginal cost given that total cost of a firm is C(q) = 60q - 12q^2 + q^3

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You need to remember that the marginal cost expresses the increase or decrease of total cost if one item more is produced.

Since the first derivative depicts the monotony of function, thus you need to differentiate the total cost function with respect to q to find the marginal cost expression such that:

`C'(q) = (60q - 12q^2 + q^3 )'`

`C'(q) = 60 - 12*2*q^(2-1) + 3*q^(3-1)`

`C'(q) = 60 - 24*q + 3*q^2`

**Hence, evaluating expression of marginal cost yields `MC = C'(q) = 60 - 24*q + 3*q^2.` **

For cost as a function of the number of products manufactured C(q), the marginal cost is the derivative of C(q) with respect to q or C'(q)

Here, C(q) = 60q - 12q^2 + q^3

C'(q) = 60 - 24q + 3q^2

**The marginal cost is C'(q) = 60 - 24q + 3q^2**